ENGM90011 Economic Analysis for Engineers 2021 Semester 1 Final Exam
This exam is worth 70% of your final grade. Exam Start: 11/06/2021 15:00 (Melbourne time)
Exam End: 11/06/2021 18:15 (Melbourne time)
Contacts: For questions about the exam (economics, clarification of question, suspected typos, etc.) please contact the lecturer via Zoom Chat (or if Chat not working). For technical questions about Zoom, etc. please contact via Zoom Chat (or if Chat not working).
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Materials allowed: Calculators are allowed. Open Book. There are eight (8) questions. Attempt all questions. There are three (3) pages including this page.
There are 100 total marks (marks in brackets).
You may assume all prices and income are positive. Show your work. Software results not accepted. Best of luck.
This exam has 15 minutes of reading time: You can read and write in this period (unlike in the closed book
invigilated exams we usually have). Then you will have 180 minutes of exam writing time. Thus, you have a
total of 15 + 180 = 195 minutes.
At the end of the exam 11/06/2021 18:15 (Melbourne time), you will be asked to put your pens down, You
are NOT to continue to work on your exam.
Submission Time: You will then have 30 minutes from 11/06/2021 18:15 (Melbourne time) to 11/06/2021
18:45 (Melbourne time) to scan and upload your exam answers. Scan your hand-written answers into a
single pdf and upload your pdf file to the ENGM90011 LMS Assignments page. On each page of your
answers, legibly write your Student ID and the page number out of the total number of pages you
submitted eg page 1 of 8, page 2 of 8, etc.
A late penalty of 20% of the total mark of the exam will be applied for the first 5 minutes delay
after 11/06/2021 18:45 (Melbourne time). After that, your submission will not be accepted and will
be marked zero.
Note: You are not to discuss the exam before 12/06/2021 18:45 (Melbourne time) as Alternative Exam
Arrangement (AEA) students will be writing later.
1. Suppose Conn’s preferences for goods x1 and x2 can be represented by the utility function 𝑈(𝑥 , 𝑥 ) = 𝑥2 + 𝑥2. Prices and income are (𝑝 , 𝑝 , 𝑀).
a. Will the consumer’s choice (𝑥∗, 𝑥∗) be on the budget line? Explain. (4) 12
b. Find Conn’s consumer choice (ie demands) as a function of the prices and income p1, p2 and M: 𝑥∗(𝑝 ,𝑝 ,𝑀), 𝑥∗(𝑝 ,𝑝 ,𝑀). (12)
2. Let there be two goods x and y with prices px and py respectively, and let M be the consumer’s income. Suppose the consumer’s (own) price elasticity of demand for good x is unit elastic. Is the cross-price elasticity of demand for good y with respect to the price of good x positive, zero, or negative? Explain. (4)
3. Let there be two goods x and y with prices px and py respectively, and let M be the consumer’s income. Let the consumer’s preferences be represented by the utility function 𝑈 = 𝑚𝑖𝑛(𝑥, 2𝑦). Find the consumer’s expenditure function. Note: you cannot use the Lagrange method as the utility function is not differentiable – but you have used the min utility function before. (4)
4. Let 𝑔: 𝑅 → 𝑅 be a strictly increasing function. Prove g is a quasiconcave function. (4)
5. A firm produces output y using two factors of production (inputs), labour L and capital K. The
firm’s production function is 𝑓(𝐿, 𝐾) = √𝐿 + √𝐾 = 𝐿2 + 𝐾2. The wage rate w = 6 and the
rental price of capital r = 2 are taken as parameters (fixed) by the firm.
a. Show whether this firm’s technology exhibits decreasing, constant, or increasing
returns to scale. (4)
b. Solve the firm’s long run cost minimization problem to derive this firm’s demand function for labour L = L(y) and for capital K = K(y), and the firm’s long run total cost function C = C(y). (8)
c. Suppose in the short run, capital is fixed at K = 100. Derive the firm’s short run total cost function C = C(y). You may assume 𝐿 ≥ 0. (5)
d. Derive this firm’s short run supply function y = y(p) assuming it is a competitive firm. Note: p is the price of the output y. (5)
6. Suppose the Australian market demand for electricity is 𝑄𝑑 = 90 − 20𝑝 where p is the price per megawatt hour (MWh). Suppose the Australian market supply of electricity is 𝑄𝑠 = 10𝑝.
a. Find the competitive market equilibrium price and quantity of electricity in Australia.
b. Because of the Covid pandemic, the Australian government provides a subsidy of
$1.50 per MWh of electricity. Find the new market equilibrium with the subsidy. (8)
c. Comparing the equilibrium with the subsidy to the equilibrium without the subsidy,
find the gains or losses to … (8)
i. Australian consumers,
ii. Australian producers,
iii. and Australia as a whole.
7. You purchase a first edition of ’s The Wealth of Nations today for $100. One year later (year 1), you anticipate you can sell it for $230. One year after that, (year 2), you would have to pay the Australian Tax Office $132 tax on your sale. Your minimum acceptable rate of return (MARR) is 15%. Be sure to show your work – a software derived answer is not acceptable.
a. Find the positive breakeven interest rates on your investment. (6)
b. Determine whether this is a pure investment. (Use only one breakeven interest rate
in your calculation – doesn’t matter which one). (2)
c. Use the internal rate of return method to determine if you should buy the book. You
may assume the project balance in year 1 is positive. (8)
d. What is the Annual Equivalent (AE) of your two-year investment? (8)
8. Let there be two goods 1 and 2. Let x1 and x2 denote their respective quantities. 𝑥 = (𝑥1, 𝑥2) represents a bundle. Milton’s preferences over bundles in 𝑅2 can be described as follows:
Between any two bundles 𝑥 = (𝑥1, 𝑥2) and 𝑦 = (𝑦1, 𝑦2), Milton prefers the bundle that has
more of good 1. If two bundles have the same amount of good 1, he prefers the bundle that has more of good 2. (Obviously, bundles with the same amount of goods 1 and 2 are the same bundle).
a. Do Milton’s preferences satisfy the strong monotonicity assumption? Prove or provide a counterexample. (4)
b. Draw the upper contour set for a bundle x. Note: it must be hand drawn on your answer paper. As such, do not worry about accuracy or scale. But label your axes and be clear which bundles are in the upper contour set for a bundle x. (4)
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